Problem: Simplify the following expression: $r = \dfrac{9x}{10} - \dfrac{x}{2}$
Solution: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $10$ and $2$ $\lcm(10, 2) = 10$ $ r = \dfrac{1}{1} \cdot \dfrac{9x}{10} - \dfrac{5}{5} \cdot \dfrac{x}{2} $ $r = \dfrac{9x}{10} - \dfrac{5x}{10}$ $r = \dfrac{9x -5x}{10}$ $r = \dfrac{4x}{10}$ Simplify the expression by dividing the numerator and denominator by 2: $r = \dfrac{2x}{5}$